Torsion gravimeter



April 7, 1942. J, M.l CRAWFORD. *E1-M 2,2793261 f TORSION GRAYIMETERl Filled oct. 25, 19:59A 2 sheets-sheen April 7,1941 I J. M. CRAWFORD ET AL 2,279,251

TORSIN GRAVIMETER Filed Oct. 25, 1939 2 Sheets-Shea?I 2 Patented Apr. 7v 1,942

U-Nirl-:o STATES 'EOBSIOI rArENr ortica John Marion t'lrawfordA and Harold Raymond Prescott, Ponca City, Okla., assignors to Continental Oil Company, Ponca City, Okla., a cor.-

poration of Delaware Application october 25, i939, serial Nc. 301,213 'z claims. (ci. iss-1.4)

The instrument shown by Dr. Mott-smith comprises a frame supporting a torsion ber which suspends a weight armcarrying a pointer. The instrument is made entirely out of quartz to Vavoid differential expansion due to temperature changes, and the construction is such thatelastic after effect, known as elastic hystcresisf is avoided. A labilizer-ber connected to a spring arrangement at one end and tothe weight arm at the other end, is provided. The torsion ber and the labilizer ber extend at right angles lto each other and in the same horizontal plane.

` The torsion gravimeter shown in Patent` 2,130,- 648 is free from hysteresis and is stable in actualeld use, giving dependable and accurate information of the intensity of gravity variations, provided the temperature and pressure are main-i' tained sulciently-constant.

We have-shown the Mott-Smith gravimeter 1 maintained.

ever any appreciable change occurs in the total intensity of' gravity.

. A word concerning the physical explanation of r this phenomenon may/be helpful. In the con- 5 struction of the Mott-Smith gravimeter, a twist of 100 in the main torsion ber 5 may be used. 'The angular twist in the primary spring 9 cannot be very great due to, structural reasons. A value of about 5 or 10 twist in the primary k spring 9 is as large'a value as"ca`n be employed and enable the stability of the weight ar'm to be Let us suppose that the Mott- Smith instrument is moved to a place having a suicient increase in the total intensity of gravity that' thepointer arm I2 moves one degree.

It will be clear that the'twistin themain torsion j ber 5 has increased from 100 to 101J and the calibration would be in error about one percent,

provided the change in the main ber 5 were the only controlling factor. (When final-adjustments are made, the torque .exerted by the labilizer opposes that exerted by the main torsion ber, so that the resultant torque controllingthe movement of the beam as the gravitational forcel varies is the dierence between the two opposing torques.` Since the labilizer torque and main ber torque are -very nearly equal in magnitude, a slight non-linearity, in either would show up as a much 'greater fraction of the resultant in Figure 1 of the drawings,.in which a T-shaped .30 torque than 0f the Original torqueframe 3 is supported in the gravimeter housing by a clamp -2. The arms lof the framesupport the main torsion ber 5 which suspends the weight arm 1. The weight arm ,l is provided Vwith a counterbalance I4-and a pointer arm l2 carrying a pointer I2a which is viewed by a microscope l5 to read changes in gravity. The labilizer ber 8 has one end thereof securedto a primary spring 9 which is supported from a secondary spring l0. adjusting spring II- enables the tension of the main torsion ber 5 to be controlled. The weight arm 'I has a projection I3 to which quartz may be fused or from `which.quartz may be removed to adjust the balance f the arm.

The labilizer fiber 8 of the Mott-Smith gravimeter increases the period of a system causing it to be more sensitive to changes in intensity of gravity.

We have found in actual use that the Mott- Smith system does not have the same calibration characteristics at one value of the total intensity of vgravity as it has at a different value of the total intensity of gravity. 'I'he instru- It isalso Vobvious, that the more neany the' two opposing torques approach each other in magnitude, the greater the departure of the coupled system from performance predicted by a calibration taken yat a diierent angle of ro- 4o non-linearity in either torque is magnied vconsiderably as it appears in the performance characteristics of the nished instrument. It will be understood by those skilled in the 'art that it is r desirable to increase the angular twist ofthe main spring arm 9 to lat least 100 in order that the labilizer may approach the same linearity of calibration as is present in'the main ber.

Non-linear performance characteristics make it necessary to re-calibrate the instrument whenever the total intensity of gravity alters appreciably. This is a time consuming and diicult task. 'I 'his is especially true in areas where no suitable gravity stations are available, having known gravity dilerences. Furthermore, the terment,'accordingly,v` must be recalibrated, when- 554 rain being surveyed iS Often large and the lnstrument will then be in error on part of the area when the total intensity of gravity changes appreciably. This further complicates the problem of obtaining a wide area gravity survey having the required degree of reliability.

In the construction shownl in the Mott-Smith gravimeter, an initial twist of 100 in the arm of main spring 9 could not be achieved and, at the same time, maintain proper instrumental stability. The spring arm in such case would have to be very light and imsy in order to obtain the small force needed, when it would move laterally as the beam changed with the total change of intensity of' gravity. Furthermore, the light spring arm which would be required would be susceptible to seismic vibrations, resulting in the introduction of erratic forces onvthe labilizerl ber 8, which, vin turn, would cause erratic beam observations. Then, too, the characteristics vof the flimsy spring arm 9 which would be required could not be duplicated with any degree of precision. This would result in instruments having widely different performances and calibration characteristics, preventing the uniformity desired.

One object of our invention is to provide a novel gravimeter having uniform calibration characteristics for wide variations in the intensity of gravity.

Another object of our invention is to provide a torsion gravimeter which is very sensitive to minute changes in the force of gravity, which is not objectionably affected by disturbing inu.

ences and provided with a new and improved `labilizer system.

Other and further objects of our invention will appear from the following description.

In the. accompanying drawings which form' part of the instant specification and are to be read in conjunction therewith and in which like Figure 3 is a diagrammatic sectional view of a torsiongravimeter.

yFigure 4 is a. curve showing the performance features of a gravimeter of our invention.

A clamp 2 supports the quartz frame 3 of our instrument in a suitable housing provided with temperature controlling means such as a thermostatically controlled bath, well known to the art, whereby to keep the temperature within the housing at ar uniform point. The quartz framework 3 comprises two U-shaped arms 4a and l', fused to a supporti-ng arm of quartz'3' which is supported by the clamp 2. The weight arm 1a is secured toa U-shaped member 6a provided with a counterweight 6'. The weight arm and U-shaped member 6a are 'supported' by the main torsion ber which is fused at 5b to quartz adiustment spring 5c. The weight arm 'la has an extension 12a forming a pointer which is viewed by a microscope A5. An extension I3a is fused to one end of the labilizer ber 8. The other end of the libilizer ber is' fused to the arm 21 of a symmetrical quartz cross 26. The cross 26 is suspended by labilizer torsion ber 25, the ends of which are fused toone arm 4' at 25a and to adjusting spring 25o at 25h. The cross'26 isrof tated to give the proper twist, thus insuring the lrequired small force on the labilizer ber 8. .The V upper arm 28 and the lowerarm 21 of the cross 75 are substantially equal in mass, size and length so that the system is balanced so far as gravity pulls are concerned. In this manner, it will be clear that variations of .total gravity will not, as far as the labilizer itself is concerned, cause a change of force on the ber l. The labilizer torsion ber 2i may be tightened to give a vibrational frequency ofthe labilizer cross 2i in excess of 100 cycles. 'Ihis makes the labilizer quite stable so far as the low frequency, large amplitude seismic vibrations are concerned, as well as giving the labilizer excellent stability in all directions. The size oi the labilizer torsioniiber 25 and the length of arms 21 and `28 are selected to give excellent linear characteristics with wide changes in total gravity. The initial twist ofthe labilizer torsion ber 2l may be as great as several complete turns if such linearity is required. In practice, we nd that a twist from 100 to 200,is sufficiently linear. The torsion ber 5 and the labilizer 8 may be in the same horizontal plane so that the labilizer ber will pass through the axis of the torsion ber. It is understood, of course; that the torsion bers, weight arms, and framework are all made out of the same material, preferably quartz.

Referring now to Figure 3, let l equal the distance from the center of gravity of the beam la to the main torsion ber. Let ma represent the weight of the beam 1a. Let 6 represent the angle from the position of zero twist in' the main ber to the angle a.

The equation of equilibrium may be expressed as follows:

' Where mgl cos(a+0),=torque caused by gravity For this case the labilizer force is not linear and this complicates the mathematical treatment of performance and calibration data.

However, with the labilizer system disclosed the labilizer torque is substantially linear and may be expressed simply as: Labilizer torque=kz0.

For this case the `equilibrium equation is: (2) mgl COS(a-} 0) :161(6-0) +1629 Using partial derivatives the following is found:

(3) gdk-mgl sin (Hannan-ado (4) g-dF-mgzsn (Home g [ti-n (a+a)(1+-)+K/ (a4-a) In normal use the level '(alis held constant from one eld station to another such that t d6 l Y g-v [tari (a4-HKM@ (af-Hill Constant a 'This is the equation of gravity sensitivity.

At any given neld station, with the gravity (g) constant, the performance of the beam (6) may be determined when the level (a) is varied.

Constant g d i (13) ESF 1+KTT1`Z onstait 9 '.lliis is the equation of level sensitivity.

From Equation i2 we'also obtain: 14) g @Mmmm-iwi Yda (15) y t 4 g tarios-t0) 2% mi oos(ml6) T-l-l) Substituting this in the Equation 11 give when a+@ is small:

This isla straight line relation betweengravity sensitivity (d0/dg) and level sensitivity (d0/da) of slope i/gK and holds only if the individual values of dfi/da are found with g constant and' the individual values of dfi/dg are found with a constant. f

Ii in the use of the instrument, the level a is not held constant as gravity diierences are measured, we may denne:

a=ao+Ala =l0+Aa (0=-Aa) The equation of equilibrium is (from 2) mgl cOS(al-0) 761(6-0) -k26=0 mgl cos,(ao+Aa+0) -k1(6+Aa) kam-'Aal =0 'mgl c0S(ao+)-k1()kz() 'ml eos owed an-lis small such that tan (an-H9) =un+ nearly 28) Ag=+goe ao+s' +aaa e+ao This is the general equation involving thejthree variables 0, Aa and Ag.

This is valid ior linear perfo 1:, ce only.

e 4 shows the performance features of the gravimeter of our invention. Beam readings arevplotted as abscissae and level values are Now in one scheme of field use a constant value At station 'A of a may be maintained-say a1. the beam reading lwould be Ba, at station B the beam reading would be Bb and at station C the beam reading would be Bc, as shown on the Figure 3. Knowing these beam differences-and knowing the calibration characteristics of the `in; irument the gravity differences lmay be calcui From the Eouation 11 the gravity sensitivity is:4

Ii' a constant gravity sensitivity is desired: i. e.

g constant Then +0 equaloonstant.

This is a. straight une of 4s degree slope as.

` shown in Figure 4 Line of constant gravity sensitivity."

If a sensitivity to gravity represented bythe v Y' At station A a' curve of level sensitivity in-V -if it is moved along the 45 degree line and superimposed.' Likewise the station A level-sensitivity curve will match the station C level sensitivitycurve if moved along the 45 degree line and superimposed.

In the instrument where a linear labilizer has been provided as in this invention these curves willsuperimpose and therefore wide areas may be explored where the calculated gravity difierences will be correct without resorting to laborious correctivecallbration measures.

In the instrument of Patent 2,130,648, it is found that as the gravity is changed the curves will not match when moved along the 45 degree line and superimposed. It is found that one will have greater curvature than the other and this tendency becomes progressively more pronounced as greater gravity variations are included.

For such a meter laborious corrective calibration measures are desirable even in small areas and the corrective measures are necessary when large areas are explored.

In the actual case values of a and arevnot observed in radians.

Let Si. equal beam readings.

Let Si equal level readings.

LetSb equal kia. Let S1 equal &a.

If the values shown in Figure 4 are in Sb and S1 readings instead of 0 and a (radians) then the slope of the line of constant sensitivity will no longer be 45 degrees.

'Ihe angle (with the horizontal) will be equal wide changes of total gravity will result in linear" variations of the forces involved and additional calibrationsor corrective calculations are eliminated. Gravity differences can be obtained more accurately and furthermore, gravity differences as determined on adjacent areas will match or dovetail without corrective calculations because of the linear calibration characteristics of our gravimeter. The lateral stability of the labilizer torsional ber and the high vibrational frequency of the cross 26 of our system make it far .less susceptible to seismic vibrations. The construction, however, is such that it will`supply therequired small force needed.' More accuracy is normally available, particularly in areas where seismic vibrations are severe. This freedom from seismic disturbanceslallows us to employ aux- `illary temperature control equipment to greater actual temperature and the required constant temperature. As long as our system is more stable to seismic disturbances, the stirring means of the temperature control arrangement may be left in operation during the time readings are taken, resulting in a more accurate temperature control. It will be understood that certain features and sub-combinations are of utility and may be employedwithout reference to other features and sub-combinations.- Thiais contemplated by and iswithin the scope of our claims. It is further obvious that various changes may be` made in details within the scope of our claims without departing from the spirit of our invention. It is, therefore, to be understood that our invention is not to be limited to the specic details shown and described.

nHaving thus described our invention, we claim:

`1. A gravity surveying instrument including in combination a supporting means, a rst torsion ber supported by said means, a second torsion ber'supported by said means in spaced relation tofsaid rst ber, a weight arm extending substantially in a. horizontal plane xed to and carried by said lrst torsion ber, a labilizer arm Iextending substantially in a vertical plane xed tween the other pair of arms and lyingsubstantially in a plane passing through said rst torsion ber, a weight arm lying substantially in a horizontal plane extending from and supported' by said rst torsion ber, a labilizer arm lying substantially in a vertical plane extending from and supported by said second torsion ber, and

a labilizer fiber having its ends connected to said labilizer arm and said weight arm whereby the torsion in said second torsion ber will accentuate the movements of said weight arm, said support, torsion bers, weight arm, labilizer arm and labilizer ber being of the same elastic material and integrally united.

3. A gravity surveying apparatus having a rst torsion ber and a second torsion ber, a weight arm connected to said rst torsion ber and a labilizer arm connected to said second torsion ber, said labilizer arm having a counterbalancing extension, and a labilizer ber connected to said weight arm and said labilizer arm, whereby the torsion in said second ber will accentuate the movements of said weight arm, the arrangement being such as to have substantially uniform calibration characteristics.

4. .A'gravity surveying apparatus including in combination; a torsion ber, a weight arm connected to said torsion ber and extending substantially in a horizontal plane, a labilizer torsion ber, alabillzer arm extending substantially in a vertical plane carried by said labilizer torsion ber, said labilizer arm having a counterbalancing arm of equal mass, size and length extending from said labilizer armv to balance gravity pulls on said labilizer arm, and a labilizer ber connected to said labilizer arm and to said weight arm.

5. A gravity surveying apparatus including in combination aA rst torsion ber, a second torsion ber, a weight arm connected to said rst torsion ber, a labilizer arm connected to said second torsion liber supported by one pair of arms, a

labilizer torsion ber supported by the other pair of arms, a Weight arm supported by said main torsion fiber and extending, laterally therefrom, a counterbalanced labilizer arm supported by said labilizer torsion fiber, and a labilizer ber connected to said weight arm and said labilizer ar said labilizer ber and said main torsion fiber lying substantially in the same plane.

7. A gravity surveying apparatus including in combination a main torsion liber, a weight ann connected to and extending laterally from said main torsion fiber, a labilizer torsion ber, a labilizer, arm connected to and extending downwardly from said labilizer torsion ber, a counterbalance supported by said labilizer arm and extending upwardly therefrom, a labilizer ber l extending between said labilizerV arm and said weight arm and passing substantially through the axis of said main torsion ber, said main torsion ber, weight arm, labilizer torsion fiber, labilizer arm, counterbalance, and labilizer ber being of the same elastic material and integrally 15 united.

JOHN MARION CRAWFORD.

HAROLD RAYMOND PRESCOTT. 

